9. Sequences, Series, & Induction

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. 1, 5, 9, 13,...

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. a₁ = 9, d=2

Find the sum of the even integers between 21 and 45.

Write the first six terms of each arithmetic sequence.

$a_1=-8,d=5$

Find the indicated term of the arithmetic sequence with first term, , and common difference, d. Find a₁₂ when a₁ = -8, d = -2

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. a_n = a_n-1 +3, a₁ = 4

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. a₁=-20, d = -4

Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58.

Find a₁₄+b₁₂.

Show that the sum of the first n positive odd integers,1 +3 +5 + ··· + (2n − 1), ... is n².

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. 7,3,-1,-5,...

Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a₂₀₀ when a₁ = −40, d = 5.

Write the first six terms of each arithmetic sequence. a₁ = 300, d= -90

Find the sum of the first 60 positive even integers.

Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

${\sum }_{i=1}^{30}(-3i+5)$